Impedance-matching transformers for rf driven co2 gas discharge lasers

ABSTRACT

In a CO 2  gas discharge laser energized by a radio frequency (RF) power source a transformer having selectively variable output impedance is used to match output impedance of the power source to the impedance of discharge electrodes of the laser. A similar transformer can be used to impose a selective variable phase-shift on the RF power from the source. The variable impedance transformer can also be used for impedance matching between amplifier stages in the power source.

TECHNICAL FIELD OF THE INVENTION

The present invention relates in general to impedance matching a radiofrequency power supply (RFPS) to a load provided by discharge electrodesand related components in a radio frequency (RF) driven CO₂ gasdischarge laser. The invention relates in particular to impedancematching an RFPS to a load using fractional-wavelength transmissionlines in series.

DISCUSSION OF BACKGROUND ART

It is well known the for optimum power transfer from a RFPS to a load animpedance-matching circuit is required. The output power of a CO2 gasdischarge laser increases directly with increasing discharge volume. TheRF input (load) impedance of the laser varies inversely as the outputpower and decreases directly as the area of the discharge. The loadimpedance can vary between lasers within the same model family due tovariations in discharge gas pressure, spacing between the electrodes,and other factors

An impedance matching circuit may comprise by one or more LC networksconsisting of one or more discrete inductors and capacitors, a length oftransmission line or coaxial cable having a length which is a selectedfraction of a wavelength long, or a plurality of fractional wavelengthtransmission lines in a selected arrangement.

An example 10A of an impedance-matching circuit including an inductivecomponent and a capacitive component is schematically illustrated inFIG. 1A. Here, an RFPS 12 having an output impedance of 50 Ohms,represented as a resistor R_(S), is matched to a resistive load R_(L) of12 Ohms. In circuit 10A impedance matching is provided by a seriesinductor L and a parallel capacitor C. Values of L and C would beselected in accordance with the frequency of RFPS 12 as is known in theart. Impedance matching an RFPS in CO₂ gas discharge lasers is describedin detail in U.S. Pat. No. 7,540,779, assigned to the assignee of thepresent invention.

One example 10B of a prior-art impedance-matching circuit including afractional wavelength transmission line is schematically illustrated inFIG. 1B. In this circuit, a transmission line section 14, having alength of one-quarter wavelength (λ/4) at the frequency of RFPS 12, isplaced in series between R_(S) and R_(L). R_(S) and R_(L) have values 65Ohms and 50 Ohms respectively. For optimum impedance matching, λ/4transmission line 14 has a characteristic impedance of 57 Ohms, i.e.,(R_(S)*R_(L))^(1/2), and introduces a phase-shift of 90° (π/2 radians)between the output of the RFPS and the input to the dischargeelectrodes.

Another example 10C of a prior-art impedance matching circuit includinga fractional wavelength transmission line is schematically illustratedin FIG. 1C. Here there are two λ/4 transmission lines 14 and 16 inseries between R_(S) and R_(L). R_(S) and R_(L) have values 65 Ohms and12.5 Ohms respectively. For optimum impedance matching, λ/4 transmissionline 14 has a characteristic impedance of 57 Ohms, and transmission line16 has a characteristic impedance of 25 Ohms. The series combination oftransmission lines introduces a total phase-shift of 180° (π radians)between the output of the RFPS and the input to the dischargeelectrodes. A detailed description of this and other combinations offractional transmission line sections for impedance matching is providedin U.S. patent application Ser. No. 12/482,341, filed. Jun. 10, 2009,and assigned to the assignee of the present invention.

Yet another example 10D of a prior-art impedance matching circuitincluding a fractional wavelength transmission line is schematicallyillustrated in FIG. 1D. Here there are two transmission lines 17 and 19,each thereof having a length of approximately λ/12 in series betweenR_(S) and R_(L). This scheme is described in detail in a CERN Report NO.59-37 entitled “A Convenient Transformer for Matching Co-axial Lines”dated November 1959 and authored by P. Bramham. A similar arrangement isdescribed in a paper “The Twelfth-Wave Matching Transformer”, D.Emerson, QST, Vol. 81, no. 6, June 1997, pp. 43-44.

In the twelfth-wave scheme described in the above-reference papers, inorder to match a source impedance Z_(S) to a load impedance Z_(L) theapproximately twelfth-wave transmission line lengths (17 and 19 in FIG.1D) would have a characteristic impedance of Z_(L) and Z_(S),respectively. Only if Z_(S) were equal to Z_(L) would the transmissionline lengths be exactly λ/12 (0.083333λ) long. For practical cases whereZ_(S)≠Z_(L), the precise length of the two transmission-line sectionsare slightly less than an exact twelfth of a wavelength.

According to the Emerson paper, the precise electrical length, l,measured in wavelengths for each transmission line is given by anequation:

l={ArcTan [(B/(B ² +B+1))^(1/2)]}/2π  (1)

where the ArcTan value is in radians and B=Z_(s)/Z_(L). By way ofexample, if B were equal to about 4, l would be about 0.0655λ instead of0.0833λ or approximately 21% shorter in length than a twelfth of a wave.As B moves closure to unity, the length of the line moves closer to λ/12(0.0833λ).

In the example of FIG. 1D where Z_(S) and Z_(L) are 65 and 50 Ohmsrespectively, i.e., B=1.3, transmission lines 17 and 19 have a length of0.08056λ instead of 0.08333λ. In this case, the shorter length imposes a29 degree phase-shift instead of exactly the 30 degrees that would beimposed by a λ/12 transmission line. Those skilled in the art willrecognize that the transmission line lengths referred to above areelectrical lengths which include the effect of dielectric constant ofinsulating material of the transmission lines.

At RFPS frequencies typically used in CO₂ gas discharge lasers, forexample, between about 40 megahertz (MHz) and about 150 MHz, the size ofthe discrete LC components in the example of FIG. 1A, is too large, andthe length of the ¼ wave transmission lines in the examples of FIGS. 1Band 1C are too long to be compatible with modern, solid-state RFPSpackaging technology. By way of example, at an RFPS frequency of 100MHz, the wavelength in free space is 3 meters. Allowing for a velocityfactor in the transmission line of 0.66, the physical transmission linelength for an electrical length of one-wavelength is still 1.98 meters,resulting in a λ/4 wavelength line of 0.495 meters, which is stillsomewhat longer than desirable. The two cascaded (series) λ/12 lines ofthe arrangement of FIG. 1D, however, would have a total length of lessthan λ/6 wavelength for a physical length of less than about 0.33meters, which is more practical for solid-state RFPS packaging.

A particular disadvantage of all of the above-described prior-artimpedance matching schemes is an inability to easily fine-adjust theimpedance matching circuit to compensate for above discussed impedancematching variations between lasers of a particular model or family. Ifthis disadvantage could be eliminated in the arrangement of FIG. 1D, theresulting arrangement would be very useful in the manufacture offamilies of CO₂ gas discharge lasers.

SUMMARY OF THE INVENTION

The present invention is directed to an electrical circuit foroptimizing transfer of RF power between a source thereof having asource-frequency and a load. In one aspect, a circuit in accordance withthe present invention comprises first and second transmission-linesections each thereof having first and second opposite ends. The firstend of the first section is connected to the source. The second end ofthe first section is connected to the first end of the second sectionvia a node therebetween. The second end of the second section isconnected to the load. Each of the first and second transmission-linesections has an electrical length equal to or less than aboutone-twelfth of a wavelength at the source-frequency. An electricalcomponent having an electrical characteristic is connected to the nodebetween the first and second transmission line sections, with theelectrical characteristic being selectively variable for optimizingtransfer of the RF power between the source and the load.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, schematically illustrate a preferredembodiment of the present invention, and together with the generaldescription given above and the detailed description of the preferredembodiment given below, serve to explain principles of the presentinvention.

FIG. 1A schematically illustrates a first prior-art circuit forimpedance matching an RF source to a load, the circuit includingdiscrete inductive and capacitive components.

FIG. 1B schematically illustrates a second prior-art circuit forimpedance matching an RF source to a load, the circuit including asingle length of transmission line, having an electrical length ofone-quarter wavelength at the frequency of the source.

FIG. 1C schematically illustrates a third prior-art circuit forimpedance matching an RF source to a load, the circuit including twolengths of transmission line in series each thereof having an electricallength of one-quarter wavelength at the frequency of the source.

FIG. 1D schematically illustrates a fourth prior-art circuit forimpedance matching an RF source to a load, the circuit including twolengths of transmission line in series each thereof having an electricallength of about one-twelfth of a wavelength at the frequency of thesource.

FIG. 2 schematically illustrates one preferred embodiment of a CO₂ laserin accordance with the present invention in which impedance matchingbetween an RF source and a laser head is accomplished by a transformerincluding two lengths of transmission line in series each thereof havingan electrical length of less than one-twelfth wavelength at thefrequency of the source with a node therebetween shunted to ground via avariable capacitor for varying the output impedance of the transformerto match that of the laser head.

FIG. 3 schematically illustrates another preferred embodiment of a CO₂laser in accordance with the present invention similar to the laser ofFIG. 2 but wherein in the impedance-matching transformer the variablecapacitor of FIG. 2 is replaced by a third length of transmission linehaving incrementally variable length for varying the output impedance ofthe transformer to match that of the laser head.

FIG. 4 schematically illustrates yet another preferred embodiment of aCO₂ laser in accordance with the present invention in which impedancematching between an RF source and a laser head is accomplished by atransformer and an impedance matching network, the transformer includingtwo lengths of transmission line in series each thereof having anelectrical length of less than one-twelfth wavelength at the frequencyof the source with a node therebetween shunted to ground via a variableinductance for varying the output phase of the transformer to optimizetransmission to the impedance matching network.

FIG. 5 schematically illustrates still another preferred embodiment of aCO₂ laser in accordance with the present invention similar to the laserof FIG. 2 but wherein the RF source includes four power amplifiers theoutputs of which are combined by a power combiner, with the transformermatching the impedance of the power combiner to the impedance of thelaser head

FIG. 6 is a plan view schematically illustrating a micro-stripimplementation of the variable impedance matching transformer of FIG. 2on an alumina substrate

FIG. 7 schematically illustrates one preferred embodiment of an RF powersupply in accordance with the present invention including an RFoscillator the output of which is amplified in sequence by apreamplifier a driver amplifier and a power amplifier, and wherein thevariable impedance matching transformer of FIG. 6 is used to impedancematch the output impedance of the driver amplifier to the inputimpedance of the power amplifier.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, wherein like components are designated bylike reference numerals, FIG. 2 schematically illustrates of onepreferred embodiment 20 of a CO₂ laser including one example 22A of avariable impedance matching transformer in accordance with the presentinvention.

A power amplifier 24 is the final amplification stage of an RF powersupply (RFPS) including an RF oscillator (not shown) the output of whichis amplified by a series of preamplifiers (also not shown) and thenpower amplifier 24. The output of the power amplifier, i.e., the outputof the RFPS, is delivered to a CO₂ laser head 26 via impedance matchingtransformer 22A. Laser head 26 includes an enclosure in which arelocated discharge electrodes and a lasing gas mixture (not shown) as isknown in the art. Here it is assumed that power amplifier 24 has animpedance Z_(S) equal to 50 Ohms, and that the laser head has animpedance Z_(L), which can have any value between 25 Ohms (Z_(MAX)) and12 Ohms (Z_(MIN)).

Transformer 22A includes two lengths of transmission line 28 and 32,each of which has the same electrical length. That length is less thanone-twelfth of a wavelength (0.0833λ) at the frequency of the RFPS. Inthis example, the transmission line length is about 0.0722λ and eachlength imposes a phase shift of 26° on a transmitted wave. A variableshunt-capacitor C_(V) has one plate 27A thereof connected to a node 30,between transmission lines 28 and 32 and the opposite plate 27Bconnected to ground. In this example, the value of C_(V) can be variedbetween 1.5 picofarads (pF) and 30 pF to match any impedance in therange between 25 Ohms and 12 Ohms. Such a range of load impedances isrepresentative of diffusion cooled slab CO₂ laser having output powerbetween about 70 Watts (W) and 250 W, respectfully. For a lasermanufacturer, being able to cover such a range of laser output-powerswith one transmission-line length reduces parts inventory in themanufacturing process.

The length of the transmission lines sections is determined by anequation

l={ArcTan [(A/(A ² +A+1))^(1/2)]}/2π  (1)

where the ArcTan value is in radians andA=Z_(S)/(Z_(MAX)*Z_(MIN))^(1/2).

FIG. 3 schematically illustrates another preferred embodiment 20A of aCO₂ laser in accordance with the present invention. Laser 20A is similarto laser 20 of FIG. 2, with an exception that variable impedancetransformer 22A of laser 20 is replaced in laser 20A by a variableimpedance transformer 22B. Variable impedance transformer 22B is similarto variable impedance transformer 22A with an exception that variablecapacitor C_(V) is replaced in transformer 22B by an open-endedtransmission-line shunt or stub 32 of incrementally variable length. Thevariability here is achieved by forming transmission line 32 from aplurality of sections, here designated 33, 34 and 35. In this exampleall of the sections have a characteristic impedance of 20.0 Ohms and thelength can be varied from zero to 0.0611λ, i.e., zero to 22° in phaseterms. If the stub has zero length, then transformer 22B matches a 25Ohm load. If a length of 22° is used for the stub length, transformer22B matches a 12 Ohm load. Intermediate impedance values are achieved bydifferent intermediate lengths of the transmission-line stub.

In embodiments of the present invention discussed above, a transformeris provided between a source and a load in which the magnitude of theoutput impedance can be varied to match some particular load impedance.It is also possible to construct a transformer in accordance with thepresent invention in which the magnitude of the impedance is fixed, butthe output phase of the transformer is variable.

By way of example FIG. 4 schematically illustrates yet anotherembodiment 40 of a laser in accordance with the present invention inwhich RF power from an RF power supply, represented by power amplifier24, is delivered to a CO₂ laser head 26 via a variable-phase transformer42 in accordance with the present invention and a fixed impedancematching network or transformer 44. Here, the power amplifier has asource impedance Z_(S) of 50 Ohms and the laser head has a loadimpedance Z_(L) of 4 Ohms. Such a low impedance is characteristic ofhigh-power diffusion-cooled slab CO₂ lasers have a large discharge area.Impedances less than 2 Ohms or less are experienced in CO₂diffusion-cooled slab lasers having about 1000 W or more of outputpower.

The input impedance of impedance-matching network 44 is 50 Ohms which isthe same as the source impedance of amplifier 24. Transformer 44includes two lengths of transmission line 46 and 48 each having acharacteristic impedance of 50 Ohms. Each has an electrical length of0.0667λ, i.e., λ/15, or 24° in phase terms. Phase variability isprovided by a variable inductance L_(V) having one end 49A thereofconnected to node 30 between the lengths of transmission line andopposite end 49B thereof connected to ground. Varying L_(V) between 40nanohenries (nH) and 500 nH varies the phase-shift imposed bytransformer 42 between +5° and +70°. This variability can be used tooptimize power by cancelling any phase shift introduced in theimpedance-magnitude matching network 44.

Those skilled in the art will recognize without further detaileddescription or illustration that fixed impedance-matching network 44 inlaser 40 could be replaced with any above-described or other embodimentof a variable impedance transformer in accordance with the presentinvention. This would provide a manufacturer with independent control ofboth the impedance-magnitude and phase of RF power at the laser head.

In the embodiments of FIGS. 2, 3, and 4 described above, the value rangefor the electrical components shunting the two lengths of transmissionline was calculated by setting up the circuit theoretically on a Smithchart. Values indicated from the Smith Chart were then refined bycircuit-simulation software PSpice® available from Cadence® Inc. of SanJose, Calif. Alternatively the Smith chart evaluation could be omittedand the values determined by simulating the appropriate circuit on amore comprehensive circuit-simulation software such as ADS availablefrom Agilent Technologies, of Santa Clara, Calif. In the embodiment ofFIG. 4, this circuit refinement recommended lengths for the two lengthsof transmission line different from those which would have beenpredicted by equation (2).

The final value for the electrical shunting component would typically bedetermined during the process of assembling the laser. This adjustmentcan be based on actual measurements of the associated components orthrough trial and error testing. For example, during set up, thecapacitance of the variable capacitor in the transformer 22A can beincreased or decreased. Where the capacitor is formed from a strip asshown in FIG. 6 discussed below, adjustments to the value of thecapacitor can be made by etching away links between capacitor segmentsor by soldering bridges between segments of the capacitor to form newlinks.

In high-power CO₂ lasers, final power amplification is often performedby dividing the output of a pre-amplifier stage into parallel channelseach including a power amplifier, the combining the outputs of the poweramplifiers with a power combiner. FIG. 5 schematically illustrates stillanother embodiment 50 of a CO₂ laser including a variable impedancetransformer in accordance with the present invention. Laser 50 issimilar to laser 20 of FIG. 2 with an exception that RF power for thelaser head is supplied from a power combiner 52 which combines theoutputs of four power amplifiers 24 as discussed above. Power combinersare well known in the art and a detailed description thereof is notnecessary for understanding principles of the present invention. Adetailed description of such combiners is provided in U.S. Pre-grantpublication No. 2008/0204134, assigned to the assignee of the presentinvention and the complete disclosure of which is hereby incorporated byreference.

As each of the power amplifiers has a source impedance of 50 Ohms, theeffective impedance of the combiner is 12.5 Ohms. Laser head 26 in thisembodiment is assumed to be of the high power type discussed above andcan have a load-impedance between 6 Ohms and 2.5 Ohms. The values ofcomponents of transformer 22A in laser 50 are changed from the values oftransformer 22A in laser 20 for this reason. Here, transmission-linesections 26 and 28 have characteristic impedances Z₀ of 6 Ohms and 12.5Ohms, respectively, and each has a length of 0.0661λ (23.8° in phaseterms). The upper capacitance limit of capacitor C_(V) is increased from30 pF to 140 pF.

In any of the above described impedance-magnitude or phase-variabletransformers, transmission-line sections could be lengths of co-axialcable or some other form of transmission line such parallel-pair ormicro-strip transmission lines. Micro-strip lines are particularlycompatible with modern solid-state RF packaging technology. Adescription of a micro-strip implementation of transformer similar totransformer 22A of FIG. 2, but designed for tuning between 9 Ohms and 12Ohms, is set forth below with reference to FIG. 6.

Here, variable impedance transformer 22A is printed on one side (shown)of an alumina substrate 60 having a thickness of 0.06 inches. Thetransformer is designated by a reference numeral 22A_(M) to reflect themicro-strip implementation thereof. The opposite side would be metalizedto provide a ground connection. The substrate measures 3.2 inches by 2.7inches. It is assumed that the input frequency to the transformertransformed is 100 MHz. Each of transmission lines 28A and 32A has anelectrical length of 0.0622λ, i.e., 23° in phase-terms. The physicallengths of lines 28A and 32A are 2.8 inches and 3.0 inches respectively.Line 28A has a width of 0.186 inches providing a characteristicimpedance of 25 Ohms. Line 32A has a width of 0.057 inches providing acharacteristic impedance of 50 Ohms.

Variable capacitor C_(V), here, comprises a primary printed capacitor 62and additional discrete printed capacitor elements 64. Capacitor 62 hasdimensions 0.9 inches by 0.9 inches providing a capacitance of 30 pF.The additional discrete capacitors have dimensions 0.49 inches by 0.125inches and each have a capacitance of 2.5 pF. Electrically connectingone or more of discrete printed capacitors 64 to primary printed 30 pFcapacitor 62 enables the net capacitance of C_(V) to be incrementallyadjusted from 30 pF to 45 pF to adjust the output impedance from 12 Ohmsto 9 Ohms. In deploying the transformer one side of the capacitors 62and 64 would be connected to ground via the metalized (not shown)surface. If primary capacitor 62 and associated discrete capacitors wereincorporated in a separate discrete high-power capacitor with suitableline impedances, the output impedance could be made incrementallyadjustable over a range from 12 Ohms to 2.5 Ohms.

As discussed above, RF power supplies for high power CO2 lasers usuallyinclude cascaded amplifiers incrementally amplifying the output of an RFoscillator. In a final stage the amplified RF can be divided intoparallel channels each including a power amplifier with the outputs ofthe power outputs being recombined by a power combiner. In suchamplifier arrangements, amplifier stages are usually cascaded without anadjustment capability for precisely matching impedances between themodules. Such impedance-matching adjustment between stages is notusually performed, because performing the match with prior-arttechnology is too time-consuming. Such a lack of impedance-matchingadjustment results in a distribution of impedance mismatches between thetransistor modules. This, in turn, results in a difference in outputpower between the modules. This difference in output power between thestages stresses the stages and causes a decrease in RF output efficiencybecause of power losses within the power combiner.

The convenient size and ease of impedance adjustment makes a variableimpedance transformer configured according to arrangement of FIG. 6useful for adjusting impedance matching between amplifier stages. Adescription of such inter-stage impedance-matching is set forth belowwith reference to FIG. 7

Here, an RFPS 70 includes a 100 MHz RF oscillator 72, the output ofwhich is sequentially amplified by a preamplifier 74, a driver amplifier76, and a power amplifier 24. The power amplifier, here, is designatedby the same reference numeral as in above-described embodiments of thepresent invention for consistency of description but can be consideredthe “load” in this embodiment. Only one preamplifier stage is depictedin FIG. 7 for simplicity of illustration. In practice, there wouldusually be more than one preamplifier, with the number of preamplifiersdependent on the power required to operate the driver and poweramplifiers in a saturation mode for high efficiency. Here, the outputpower of the driver amplifier is considered sufficiently high thatimpedance matching between the driver amplifier and the power amplifieris justified to obtain efficient operation of the RFPS. Impedancematching is provided by transformer 24A_(M) of FIG. 6.Incrementally-variable capacitor C_(V) is grounded by connection 78.

In embodiments of the present invention described above twotransmission-line sections are connected in series. An electricalcomponent having an electrical characteristic is connected to the nodebetween the two transmission-line sections, with the electricalcharacteristic being selectively variable for optimizing transfer of theRF power between the source and the load. Those skilled in the art willrecognize without further detailed description or illustration that asingle electrical component could be replaced by a combination ofsimilar components arranged to provide the same electricalcharacteristic. By way of example, a single transmission line sectioncould be replaced by a parallel pair of sections, or a single capacitorcould be replaced by a parallel pair of capacitors. Any suchcombinations can be made without departing from the spirit and scope ofthe present invention.

In summary the present invention is described above with reference to apreferred and other embodiments. The invention, however, is not limitedto the embodiments described and depicted, herein. Rather the inventionis limited only by the claims appended hereto.

1. An electrical circuit for optimizing a transfer of RF-power between asource thereof having a source-frequency, and a load, the circuitcomprising: first and second transmission-line sections each thereofhaving first and second opposite ends, with the first end of the firstsection being connected to the source, the second end of the firstsection being connected to the first end of the second section via anode therebetween, and the second end of the second section beingconnected to the load, with each of the first and secondtransmission-line sections having an electrical length equal to or lessthan about one-twelfth of a wavelength at the source-frequency; and anelectrical component having an electrical characteristic connected tothe node between the first and second transmission-line sections, withthe electrical characteristic of the component being selectivelyvariable for optimizing the transfer of the RF-power between the sourceand the load.
 2. The circuit of claim 1, wherein the electricalcomponent is a capacitor having a selectively variable capacitance. 3.The circuit of claim 2, wherein the capacitor has first and secondopposite plates with the first plate being connected to the node betweenthe first and second transmission-line sections and the second platebeing connected to ground.
 4. The circuit of claim 2, wherein thetransformer has an output-impedance and varying the capacitance of thecapacitor varies the output-impedance of the transformer.
 5. The circuitof claim 1, wherein the electrical component is a thirdtransmission-line section having first and second opposite ends and aselectively variable electrical-length.
 6. The circuit of claim 5,wherein the first end of the third transmission-line section isconnected to the node between the first and second transmission-linesections and the second end of the third transmission-line section isopen.
 7. The circuit of claim 6, wherein the transformer has anoutput-impedance and varying the electrical-length of the thirdtransmission line section varies the output-impedance of thetransformer.
 8. The circuit of claim 6, wherein the electrical length ofthe third transmission line section is less than about one-twelfth of awavelength at the source frequency.
 9. The circuit of claim 1, whereinthe electrical component is an inductor having a selectively variableinductance.
 10. The circuit of claim 9, wherein the inductor has firstand second opposite ends the first plate being connected to the nodebetween the first and second transmission line sections and the secondend being connected to ground.
 11. The circuit of claim 9, wherein thetransformer imposes a phase-shift on the RF power delivered by thesource and varying the inductance of the inductor varies the phase-shiftimposed by the transformer.
 12. An electrical circuit for optimizing atransfer of RF-power between a source thereof having a source-frequencyand a source impedance, and a load having a load impedance, the circuithaving an input impedance and an output impedance and comprising: firstand second transmission-line sections each thereof having first andsecond opposite ends with the first and second transmission-linesections each thereof having a characteristic impedance, the first endof the first section being connected to the source, the second end ofthe first section being connected to the first end of the second sectionvia a node therebetween, and the second end of the second section beingconnected to the load, with each of the first and secondtransmission-line sections having an electrical length equal to or lessthan about one-twelfth of a wavelength at the source-frequency; acapacitor connected to the node between the first and secondtransmission-line sections, the capacitance of the capacitor cooperativewith the electric length and characteristic impedances of thetransmission line sections determining the output-impedance of thecircuit; and wherein the capacitance of the capacitor is selectivelyvariable for varying the output-impedance of the circuit to match theload-impedance thereby optimizing the transfer of the RF-power betweenthe source and the load.
 13. The circuit of claim 12, wherein theload-impedance has a value between a maximum anticipated value and aminimum anticipated value and the capacitance of the capacitor isvariable between a minimum value and a maximum value, wherein thecharacteristic impedance of the first transmission-line section is aboutequal to the maximum anticipated value of the load-impedance, thecharacteristic impedance of the second transmission-line section isabout equal to the source-impedance, and wherein varying the capacitanceof the capacitor between the minimum and maximum values thereof variesthe output impedance of the circuit between the maximum and minimumvalues, respectively, thereof.
 14. The circuit of claim 13, wherein thesource-impedance is 50 Ohms, the maximum and minimum values ofload-impedance are 25 Ohms and 12 Ohms respectively, the minimum andmaximum capacitance values of the capacitor are about 1.5 picofarads andabout 30 picofarads respectively.
 15. An electrical circuit foroptimizing a transfer of RF-power between a source thereof having asource-frequency and a source impedance, and a load having a loadimpedance, the circuit imposing a phase-shift on the RF powertransferred thereby, the circuit comprising: first and secondtransmission-line sections each thereof having first and second oppositeends with the first and second transmission-line sections each thereofhaving a characteristic impedance, the first end of the first sectionbeing connected to the source, the second end of the first section beingconnected to the first end of the second section via a nodetherebetween, and the second end of the second section being connectedto the load, with each of the first and second transmission-linesections having an electrical length equal to or less than aboutone-twelfth of a wavelength at the source-frequency; an inductorconnected to the node between the first and second transmission-linesections, the inductance of the inductor cooperative with the electriclength and characteristic impedances of the transmission line sectionsdetermining the phase-shift imposed by the circuit on the transferred RFpower; and wherein the inductance of the inductor is selectivelyvariable for varying the phase shift imposed by the circuit therebyoptimizing the transfer of the RF-power between the source and the load.16. The circuit of claim 15, wherein the phase-shift has a value betweena minimum desired value and a maximum desired value and the inductanceof the inductor is variable between a minimum value and a maximum value,wherein the characteristic impedance of the first transmission-linesection is about equal to the load-impedance, the characteristicimpedance of the second transmission-line section is about equal to thesource-impedance, and wherein varying the inductance of the inductorbetween the minimum and maximum values thereof varies the phase-shiftimposed by the circuit between the minimum and maximum values,respectively, thereof.
 17. The circuit of claim 16, wherein thesource-impedance is 50 Ohms, the load-impedance is 50 Ohms respectively,the minimum and maximum inductance values of the capacitor are about 40nanohenries and 500 nanohenries, and the minimum and maximumphase-shifts are +5° and +70°.